Question

If a labourer earns Rs.672 per week, how much will he earn in 18 days?

Answer 1

Hint: To solve this question, we should know the concept of proportionality of two parameters. Here, in the question, the number of days of work of a labourer is directly proportional to the money he earns. From this principle, we can get the wage of 1 day of work and then multiply it with 18 to get the salary of 18 days.

Complete step-by-step answer:
Consider two parameters F and G which are directly proportional to each other. This means that F increases or decreases linearly with G increasing or decreasing respectively. Numerically, directly proportional is shown as$F\propto G$. As the two parameters are linearly related, we can assume a constant of proportionality K which is used to get an equation.
$\begin{align}
  & F\propto G \\
 & F=KG\to \left( 1 \right) \\
\end{align}$
By using the initial condition, we can find the constant of proportionality and we can find the required answer.
In the question, let
G – Number of days of work done by the labourer
F – Wage in rupees earned by the labourer.
From equation-1
Wage in rupees earned by the labourer = K $\times $ Number of days of work done by the labourer.
In the question it is given that the labourer earned Rs.672 for a work of week, that is 7 days.
G = 7 days, F = Rs.672
Substituting in equation-1, we get
$Rs.672=K\times 7days$
Dividing by 7 days on both sides gives
$\begin{align}
  & K=\dfrac{672}{7}\dfrac{Rs}{day} \\
 & K=96\dfrac{Rs}{day} \\
\end{align}$
Equation-1 can be written as
$F=96G\to (2)$
We have to find the salary for 18 days. So, G = 18. Substituting G = 18 in equation-2, we get
\[\begin{align}
  & F=96\times 18 \\
 & F=1728 \\
\end{align}\]
$\therefore $The money earnt for 18 days of work by the labourer is Rs.1728.

Note:The question can be solved in another way using unitary method. Unitary method is a way in which we compare the similar parameters and directly solve the question. That is if
A - B and
C - D then we can write that$\dfrac{A}{C}=\dfrac{B}{D}\to \left( 3 \right)$. Similarly,
7 days - Rs.672
18 days - $x$
Substituting in equation-3, we get
$\begin{align}
  & \dfrac{7}{18}=\dfrac{672}{x} \\
 & \\
\end{align}$
Cross-multiplying gives
\[\begin{align}
  & x=\dfrac{18\times 672}{7} \\
 & x=18\times 96 \\
 & x=Rs.1728 \\
\end{align}\]
This tally with the answer in the process of the solution.